In this paper, the application of three well-known multi-objective optimization algorithms to water distribution network (WDN) optimum design has been considered. Non-dominated sorting genetic algorithm II (NSGA-II), Multi-objective differential evolution (MODE) and Multi-objective particle swarm optimization (MOPSO) algorithms are applied to benchmark mathematical test function problems for evaluating the performance of these algorithms. The Accuracy and computational runtime are the two indicators used for the comparison of these three algorithms. The optimization results of mathematical test functions show that all three algorithms were able to accurately produce Pareto Front, but the computational time of MODE algorithm to achieve the optimal solutions is lower than the two other algorithms. Then, the discussed algorithms have been used to optimize the WDN design problem. Comparison of the generated solutions on the Pareto Front for WDN design shows that the obtained Pareto Front of MODE is more accurate and faster.

Resilience has been increasingly pursued in the management of water distribution systems (WDSs) such that a system can adapt to and rapidly recover from potential failures in face of a deep uncertain and unpredictable future. Topology has been assumed to have a great impact on resilience of WDSs, and is the basis of many studies on assessing and building resilience. However, this fundamental assumption has not been justified and requires investigation. To address this, a novel framework for mapping between resilience performance and network topological attributes is proposed. It is applied to WDSs here but can be adaptable to other network systems. In the framework, resilience is comprehensively assessed using stress-strain tests which measure system performance on six metrics corresponding to system resistance, absorption and restoration capacities. Six key topological attributes of WDSs (connectivity, efficiency, centrality, diversity, robustness and modularity) are studied by mathematical abstraction of WDSs as graphs and measured by eight statistical metrics in graph theory. The interplay between resilience and topological attributes is revealed by the correlations between their corresponding metrics, based on 85 WDSs with different sizes and topological features. Further, network variants from a single WDS are generated to uncover the value of topological attribute metrics in guiding the extension/rehabilitation design of WDSs towards resilience. Results show that only certain aspects of resilience performance, i.e. spatial and temporal scales of failure impacts, are strongly influenced by some (not all) topological attributes, i.e. network connectivity, efficiency, modularity and centrality. Metrics for describing the topological attributes of WDSs need to be carefully selected; for example, clustering coefficient is found to be weakly correlated with resilience performance compared to other metrics of network connectivity (due to the grid-like structures of WDSs). Topological attribute metrics alone are not sufficient to guide the design of resilient WDSs and key details such as the location of water sources also need to be considered.